Question: What is the 3-digit number which is divisible by 10?<br>Statement-I:<br>If the digits in hundred's place and ten's place of the number are interchanged, the resulting number is diminished by 180.<br>Statement-II:<br>If the digit in hundred's place is halved and digit in ten's place and unit place of the number are interchanged, the resulting number is diminished by 336.

Consider the following for the next ten (10) items that follow :<br>Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.<br>Mark option (b) if the question can be answered by using either statement alone.<br>Mark option (c) if the question can be answered by using both the statements together, but cannot be answered using either statement alone.<br>Mark option (d) if the question cannot be answered even by using both the statements together.

  1. A. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone ✓
  2. B. The question can be answered by using either statement alone
  3. C. The question can be answered by using both the statements together, but cannot be answered using either statement alone
  4. D. The question cannot be answered even by using both the statements together

Correct Answer: A. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone

Explanation

Let the number be 100a+10b+c. Since it is divisible by 10, c=0. Statement-I: 100a+10b - (100b+10a) = 90(a-b) = 180 \implies a-b=2. Not sufficient. Statement-II: The new number is 100(a/2) + 10(0) + b = 50a+b. The difference is 100a+10b - (50a+b) = 50a+9b = 336. Checking single digits, only a=6, b=4 works (300+36=336). The number is 640. Statement-II alone is sufficient.

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